Related papers: Detecting Potential Instabilities of Numerical Alg…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…
Designing a stabilizing controller for nonlinear systems is a challenging task, especially for high-dimensional problems with unknown dynamics. Traditional reinforcement learning algorithms applied to stabilization tasks tend to drive the…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…
This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
The unprecedented success of deep learning (DL) makes it unchallenged when it comes to classification problems. However, it is well established that the current DL methodology produces universally unstable neural networks (NNs). The…
This paper is about the surprising interaction of a foundational result from model theory, about stability of theories, with algorithmic stability in learning. First, in response to gaps in existing learning models, we introduce a new…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…
Stability is a general notion that quantifies the sensitivity of a learning algorithm's output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to…
Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is…
Many machine learning algorithms rely on iterative updates of uncertainty representations, ranging from variational inference and expectation-maximization, to reinforcement learning, continual learning, and multi-agent learning. In the…
Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is insensitive to small perturbations in the training set such…